sqrt(1-sinx)=sqrt(sin^2(x/2)+cos^2(x/2)-2.sin(x/2)cos(x/2)√1−sinx=√sin2(x2)+cos2(x2)−2.sin(x2)cos(x2)color(green)([As.sin^2theta+cos^2theta=1andsin2theta=2sinthetacostheta])[As.sin2θ+cos2θ=1andsin2θ=2sinθcosθ]
=sqrt((sin(x/2)-cos(x/2))^2=√(sin(x2)−cos(x2))2color(red)([As.a^2+b^2-2ab=(a-b)^2=(b-a)^2])[As.a2+b2−2ab=(a−b)2=(b−a)2]
=sin(x/2)-cos(x/2)=sin(x2)−cos(x2)color(brown)((Ans.))(Ans.)